The Obama administration has indicated it plans to build a criminal case against Dzhokhar Tsarnaev, who remains in serious condition in a hospital.

Some of Paul's congressional Republican colleagues have said Tsarnaev's rights should be more restricted than the administration intends.

Paul said after an appearance at a Louisville power plant Monday that he hopes Tsarnaev is "prosecuted to the fullest extent of the law and I hope he's ashamed and (is) punished for killing innocents."

The most serious charge available to prosecutors would be the use of a weapon of mass destruction to kill, which carries a possible death sentence.